• Communications for Statistical Applications and Methods
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• 제13권3호
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• pp.513-524
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• 2006

In this paper, we introduce a new notions of conditionally weak dependence and we study their properties, preservation of the conditionally weak independent and positive and negative quadrant dependent(CWQD) property under mixtures, limits, closure under convex combinations, and their interrelationships. Furthermore, we extend multivariate stochastic dependence to stronger conditions of dependence.

• Communications for Statistical Applications and Methods
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• 제7권3호
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• pp.845-858
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• 2000

In this paper new results are obtained for multivariate processes which help us to identify weak negative orthant dependent(WNOD) structures among hitting times of the processes. Furthermore, an approach to derive dependence properties among the processes is proposed and a partial solution to the question tat what kinds of the dependence properties, when they are imposed on processes, are reflected as analogous properties of corresponding hitting times is give. Examples are given to illustrate these concepts.

• Communications for Statistical Applications and Methods
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• 제17권6호
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• pp.829-843
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• 2010

To test for the serial dependence in time series of counts data, Jung and Tremayne (2003) evaluated the size and power of several tests under the class of INARMA models based on binomial thinning operations for Poisson marginal distributions. The overdispersion phenomenon(i.e., a variance greater than the expectation) is common in the real world. Overdispersed count data can be modeled by using alternative thinning operations such as random coefficient thinning, iterated thinning, and quasi-binomial thinning. Such thinning operations can lead to time series models of counts with negative binomial or generalized Poisson marginal distributions. This paper examines whether the test statistics used by Jung and Tremayne (2003) on serial dependence in time series of counts data are affected by overdispersion.

• Communications for Statistical Applications and Methods
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• 제27권2호
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• pp.163-175
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• 2020

We consider a wide class of general weakly-dependent processes, called ψ-weak dependence, which unify almost all weak dependence structures of interest found in statistics under natural conditions on process parameters, such as mixing, association, Bernoulli shifts, and Markovian sequences. For detecting the tail behavior of the weakly dependent processes, change point tests are developed by means of cumulative sum (CUSUM) statistics with the empirical distribution functions of sample extremes. The null limiting distribution is established as a Brownian bridge. Its proof is based on the ψ-weak dependence structure and the existence of the phantom distribution function of stationary weakly-dependent processes. A Monte-Carlo study is conducted to see the performance of sizes and powers of the CUSUM tests in GARCH(1, 1) models; in addition, real data applications are given with log-returns of financial data such as the Korean stock price index.

• Communications for Statistical Applications and Methods
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• 제2권1호
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• pp.201-208
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• 1995

In the last years there has been growing interest in concepts of positive dependence for families of random variables such that concepts are considerable us in deriving inequalities in probability and statistics. Lehman introdued various concepts of positive dependence for bivariate random variables. A much stronger notions of positive dependence were later considered by Esary, Proschan, and Walkup. Ahmed et al and Ebrahimi and Ghosh also obtained multivariate versions of various bivariate positive dependence as descrived by Lehman. See also Block al. Glaz and Johnson an Barlow and Proschan and the references there. Multivariate processes arise when instead of observing a single process we observe several processes, say $X_19t), \cdots, X_n(t)$ simultaneously. For example, in an engineering context we may want to study the simultaneous variation of current and voltage, or temperature, pressure and volume over time. In economics we may be interested in studying inflation rates and money supply, unemployment and interest rates. We could of course, study each quantity on its own and treat each as a separate univariate process. Although this would give us some information about each quantity it could never give information about the interrelationship between various quantities. This leads us to introduce some concepts of positive and for multivariate stochastic processes. The concepts of positive dependence have subsequently been extended to stochastic processes in different directions by many authors.

• Journal of the Korean Data and Information Science Society
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• 제14권2호
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• pp.413-428
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Communications for Statistical Applications and Methods
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• 제14권3호
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• pp.687-698
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• 2007

A normal mixture model with which dependence between classes is incorporated is proposed in order to detect differentially expressed genes. Gene clustering approaches suffer from the high dimensional column of microarray expression data matrix which leads to the over-fit problem. Various methods are proposed to solve the problem. In this paper, use of simple averaging data within each class is proposed to overcome the various problems due to high dimensionality when the normal mixture model is fitted. Some experiments through simulated data set and real data set show its availability in actuality.

• Journal of the Korean Statistical Society
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• 제12권1호
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• pp.10-17
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• 1983

Let $X^{(n)}_j, j=1,2,\cdots,n, n=1,2,\cdots$ be a triangular array of random variables which arise naturally in a study of ferromagnetism in statistical mechanics. This paper presents weak convergence of random function $W_n(t)$, an appropriately normalized partial sum process based on $S^{(n)}_n = X^{(n)}_i+\cdot+X^{(n)}_n$. The limiting process W(t) is shown to be Gaussian when weak dependence exists. At the critical point where the change form weak to strong dependence takes place, W(t) turns out to be non-Gaussian. Our results are direct extensions of work by Ellis and Newmam (1978). An example is considered and the relation of these results to critical phenomena is briefly explained.

• 한국안전학회지
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• 제31권5호
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• pp.95-101
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• 2016

This study proposes a multi-scale dynamic system reliability analysis of control system as a method of quantitative evaluation of its performance in probabilistic terms. In this second paper, we discuss the control effect of the viscous damper on the seismic performance of the structure-level failure. Since the failure of one structural member does not necessarily cause the collapse of the structural system, we need to consider a set of failure scenarios of the structural system and compute the sum of the failure probabilities of the failure scenarios where the statistical dependence between the failure scenarios should be taken into account. Therefore, this computation requires additional system reliability analysis. As a result, the proposed approach takes a hierarchial framework where the failure probability of a structural member is computed using a lower-scale system reliability with the union set of time-sequential member failures and their statistical dependence, and the failure probability of the structural system is again computed using a higher-scale system reliability with the member failure probabilities obtained by the lower-scale system reliability and their statistical dependence. Numerical results demonstrate that the proposed approach can provide an accurate and stable reliability assessment of the control performance of the viscous damper system on the system failure. Also, the parametric study of damper capacity on the seismic performance has been performed to demonstrate the applicability of the proposed approach through the probabilistic assessment of the seismic performance improvement of the damper system.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.647-653
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• 2015

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.